Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 7 - Functions and Graphs - 7.5 Formulas, Applications, and Variation - 7.5 Exercise Set: 71

Answer

$\color{blue}{y=\frac{5000}{x^2}}$

Work Step by Step

RECALL: (1) When $y$ varies directly as $x$, the variation is direct and is represented by the equation $y=kx$ where $k$ is the constant of variation. (2) When $y$ varies inversely as $x$, the variation is inverse and is represented by the equation $y=\frac{k}{x}$ where $k$ is the constant of variation. $y$ varies inversely as the square of $x$ so the equation is $y=\frac{k}{x^2}$ with $k$=constant of variation. To find the value of $k$, substitute the given values into $y=\frac{k}{x^2}$ to obtain: $$y=\frac{k}{x^2} \\50=\frac{k}{10^2} \\50 =\frac{k}{100} \\100(50)=k \\5000=k$$ Thus, the equation of the variation is: $\color{blue}{y=\frac{5000}{x^2}}$.
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